y^{''}-3y^'+2y=4e^{et},y(0)=-3,y^'(0)=5

Lösung

y^{^{''}} - 3 y^{^{'}} + 2 y = 4 e^{e t}, y (0) = - 3, y^{^{'}} (0) = 5

y = (- 3 + \frac{11 e ^{2} - 37 e + 30}{e ^{2} - 3 e + 2} - \frac{4}{e ^{2} - 3 e + 2}) e^{2 t} - \frac{11 e ^{2} - 37 e + 30}{e ^{2} - 3 e + 2} e^{t} + \frac{4}{e ^{2} - 3 e + 2} e^{e t}

Schritte zur Lösung

y^{''} (t) - 3 y^{'} (t) + 2 y = 4 e^{e t}

Solve linear ODE:

y = (- 3 + \frac{11 e ^{2} - 37 e + 30}{e ^{2} - 3 e + 2} - \frac{4}{e ^{2} - 3 e + 2}) e^{2 t} - \frac{11 e ^{2} - 37 e + 30}{e ^{2} - 3 e + 2} e^{t} + \frac{4}{e ^{2} - 3 e + 2} e^{e t}

y = (- 3 + \frac{11 e ^{2} - 37 e + 30}{e ^{2} - 3 e + 2} - \frac{4}{e ^{2} - 3 e + 2}) e^{2 t} - \frac{11 e ^{2} - 37 e + 30}{e ^{2} - 3 e + 2} e^{t} + \frac{4}{e ^{2} - 3 e + 2} e^{e t}

y^{^{''}} + 8 y = 2 t^{4}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 4 y^{^{'}} + 4 y = x^{- 1} e^{2 x}

16 y^{^{''}} - 24 y^{^{'}} + 9 y = 5 - 3 x

y^{^{''}} + 4 y^{^{'}} + 4 y = e^{- 2 x} \cdot x^{- 2}

y^{^{''}} + 4 y^{^{'}} + 40 y = 50 sin (6 t)